Radial segregation patterns in rotating granular mixtures: waviness selection

Influence of fine particle content in debris flows on alluvial fan morphology

Alluvial fans are large-scale depositional structures commonly found at the base of mountain ranges. They are relatively soil-rich compared to the rocky terrains, or catchment areas, from which their material originates. When frequented by debris flows (massive, muddy, rocky flows) they contribute significantly to local hazards as they carry focused, collisional, fast-moving materials across alluvial fans, unpredictable in size, speed, and direction. We research how fine particle content in debris flows correlates with directional changes, i.e., debris flow avulsions. Toward this, we analyzed field data from two neighboring alluvial fans in the White Mountains (California, USA) that exhibit dramatically different topographies despite their proximity and associated similar long-term climates. Informed by these measurements, we performed long-term and incremental alluvial fan experiments built by debris flows with systematically-varied fine particle content. We found that (1) decreasing fine particle content increases the variability of fan slopes and associated channelization dynamics, and (2) for all mixtures longer-term continuous alluvial fan experiments form more complex surface channelizations than repeated flows for the same total time, indicating the importance of both particle sizes and timescales on alluvial fan surface morphology.

Segregation patterns in three-dimensional granular flows

Flow of size-bidisperse particle mixtures in a spherical tumbler rotating alternately about two perpendicular axes produces segregation patterns that track the location of nonmixing islands predicted by a dynamical systems approach. To better understand the paradoxical accumulation of large particles in regions defined by barriers to transport, we perform discrete element method (DEM) simulations to visualize the three-dimensional structure of the segregation patterns and track individual particles. Our DEM simulations and modeling results indicate that segregation pattern formation in the biaxial spherical tumbler is due to the interaction of size-driven radial segregation with the weak spanwise component of the advective surface flow. Specifically, we find that after large particles segregate to the surface, slow axial drift in the flowing layer, which is inherent to spherical tumblers, is sufficient to drive large particles across nominal transport barriers and into nonmixing islands predicted by an advective flow model in the absence of axial drift. Axial drift alters the periodic dynamics of nonmixing islands, turning them into "sinks" where large particles accumulate even in the presence of collisional diffusion. Overall, our results indicate that weak perturbation of chaotic flow has the potential to alter key dynamical system features (e.g., transport barriers), which ultimately can result in unexpected physical phenomena.

Dynamics of bidensity particle suspensions in a horizontal rotating cylinder

We report Stokesian dynamics simulations of bidensity suspensions rotating in a horizontal cylinder. We studied the phase space and radial and axial patterns in settling as well as floating systems. Each system was composed of particle mixtures of two different densities. As many as eight unique phases are identified for each system along the radial plane. The bidensity system shows similarity to the monodisperse case only when the radial distribution of the particles is completely uniform. Characteristic behavior of the bidensity systems is identical at low rotation rates and contrasting when centrifugal force dominates. Expressing the phase boundaries in terms of dimensionless parameters U_{s}/(ΩR) and g/(Ω^{2}R) gives a linear fit unifying the data in the gravity-dominated regime. At high rotation rates, the behavior is opposing for either system though linear in nature. In the axial direction, number density profiles of both systems affirm the phenomenon of band formation. Location of the axial bands remains the same for heavy and light particles in both systems. We have also reestablished that an inhomogeneous particle configuration in the radial plane induces growing instabilities in the axial plane which amplify to form particle bands similar to monodisperse suspensions.

Granular segregation in a thin drum rotating with periodic modulation

We present the results of an experimental investigation into the effects of a sinusoidal modulation of the rotation rate on the segregation patterns formed in thin drum of granular material. The modulation transforms the base pattern formed under steady conditions by splitting or merging the initial streaks. Specifically, the relation between the frequency of modulation and the rotation rate determines the number of streaks which develop from the base state. The results are in accord with those of Fiedor and Ottino [J. Fluid. Mech. 533, 223 (2005)10.1017/S0022112005003952], and we show that their ideas apply over a wide range of parameter space. Furthermore, we provide evidence that the observed relationship is maintained for filling fractions far from 50% and generalize the result in terms of the geometry of the granular deposit.

Density-driven spontaneous streak segregation patterns in a thin rotating drum

Granular mixtures may segregate because of external driving forces, which play an important role in industry and geophysics. We investigate experimentally the mechanism of density-driven spontaneous streak segregation patterns in a thin rotating drum. We find that a spontaneous streak segregation pattern can occur in such a system, which we call a D-system. A phase diagram identifies three segregation pattern regimes in this study: the mixing regime, the core segregation regime, and the streak segregation regime.

Spin Brazil-nut effect and its reverse in a rotating double-walled drum

The segregation of binary mixtures in a filled rotating double-walled drum is explored by simulations. Based on the characteristics of self-gravity and the centrifugal force, we argue that both percolation and buoyancy effects dominate the segregation process. The simulational results show that up to long enough times the segregation state is controlled by the rotational speed, the particle radius and density. At low rotational speeds, the smaller and heavier particles tend to accumulate towards the inner drum wall and the bigger and lighter ones towards the outer drum wall, while the segregation pattern reverses completely at higher rotational speeds. Two typical phase diagrams in the space of the density and radius ratio of bigger particles to smaller particles further confirm the predictions.

Ringlike spin segregation of binary mixtures in a high-velocity rotating drum

This study presents molecular dynamics simulations on the segregation of binary mixtures in a high-velocity rotating drum. Depending on the ratio between the particle radius and density, similarities to the Brazil-nut effect and its reverse form are shown in the ringlike spin segregation patterns in radial direction. The smaller and heavier particles accumulated toward the drum wall, whereas the bigger and lighter particles accumulated toward the drum center. The effects of particle radius and density on the segregation states were quantified and the phase diagram of segregation in the ρ(b)/ρ(s) - r(b)/r(s) space was plotted. The observed phenomena can be explained by the combined percolation and the buoyancy effects.

Segregation pattern competition in a thin rotating drum

Results are presented of an experimental investigation into patterned size segregation of binary granular mixtures in a thin rotating drum that is half full. It is observed that streaks of small particles are formed within regions of large ones where the integer number of streaks is fixed over a range of rotation rate of the drum. Different patterns form in adjacent parameter ranges and the dynamics associated with the exchange between neighboring states is analyzed using angular spatiotemporal diagrams. These help to reveal properties of the merging mechanism for streaks of small particles. We report experimental evidence that the merging of streaks is mediated by the movement of a surplus material in a direction opposite to that of the rotation of the drum. The excess material is distributed throughout the pattern and the extra streak eventually disappears.

Isolating segregation mechanisms in a split-bottom cell

We study the segregation of mixtures of particles in a split-bottom cell to isolate three possible driving mechanisms for segregation of densely sheared granular mixtures: gravity, porosity, and velocity gradients. We find that gravity alone does not drive segregation associated with particle size without a sufficiently large porosity or porosity gradient. A velocity gradient, however, appears to be capable of driving segregation associated with both particle size and material density. In all cases, the final segregation state is approached exponentially.

Kinematics of densely flowing granular mixtures

We measure the kinematics of segregating granular mixtures in dense free-surface boundary-layer flow in a rotated drum. We find that in a segregating mixture, the different components move with roughly the same velocities, except for a relatively small segregation velocity perpendicular to the direction of flow. On the other hand, the mean variance of the velocities--often associated with a granular temperature--may differ for the two components. In the majority of the high-density boundary layer, the difference is driven by relative particle size and may be understood considering a geometrically motivated model. In the low-density region at the top of the boundary layer, the difference is driven by relative particle mass, similar to observations in more energetic systems.

Capturing patterns and symmetries in chaotic granular flow

Segregation patterns formed by time-periodic flow of polydisperse granular material (varying in particle size) in quasi-two-dimensional (quasi-2D) tumblers capture the symmetries of Poincaré sections, stroboscopic maps of the underlying flow, derived from a continuum model which contains no information about particle properties. We study this phenomenon experimentally by varying the concentration of small particles in a bidisperse mixture in quasi-2D tumblers with square and pentagonal cross sections. By coupling experiments with an analysis of periodic points, we explain the connection between the segregation patterns and the dynamics of the underlying flow. Analysis of the eigenvectors and unstable manifolds of hyperbolic points shows that lobes of segregated small particles stretch from hyperbolic points toward corners of the tumbler, demonstrating the connection between regions of chaotic flow and the shape of the segregation patterns. Furthermore, unstable manifolds map the shape of lobes of segregated particles. The techniques developed here can also be applied to nonpolygonal tumblers such as elliptical tumblers, as well as to circular tumblers with time-periodic forcing.

Pattern selection by a granular wave in a rotating drum

The results of an experimental investigation of granular segregation in a thin rotating drum are presented. A mechanism based on the presence of an uphill wave of particles has been found to govern the observed pattern of petals. Specifically we develop a simple model that captures the essential physics of the segregation and yields an algebraic expression that predicts the number of petals in the pattern.